## Pressure

Category : UPSC

Pressure

1.           Mechanical Properties of Solids and Fluids

• The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed, is known as elasticity and the deformation caused is known as elastic deformation.
• However, if we apply force to a lump of putty or mud, they have no gross tendency to regain their previous shape, and they get permanently deformed. Such substances are called plastic and this property is called plasticity.
• Pressure is a scalar quantity. The SI unit of pressure is N m-2 has been named as pascal (Pa).
• A common unit of pressure is the atmosphere (atm), i.e. the pressure exerted by the atmosphere at sea level (1 atm $=1.013\times {{10}^{5}}$ Pa).
• Density is a positive scalar quantity. A liquid is largely incompressible and its density is therefore, nearly constant at all pressures. Gases, on the other hand exhibit a large variation in densities with pressure.
• The density of water at 4°C (277 K) is $1.0\times {{10}^{3}}$ kg m-3. The relative density of a substance is the ratio of its density to the density of water at 4°C.
• The pressure of the atmosphere at any point is equal to the weight of a column of air of unit cross sectional area extending from that point to the top of the atmosphere. At sea level it is $1.013\times {{10}^{5}}$ Pa (1 atm).
• The mm of Hg and torr are used in medicine and physiology. In meteorology, a common unit is the bar and millibar.
• An open-tube manometer is a useful instrument for measuring pressure differences.
• In reality the density of air decreases with height. So does the value of g. The atmospheric cover extends with decreasing pressure over 100 km. We should also note that the sea level atmospheric pressure is not always 760 mm of Hg. A drop in the Hg level by 10 mm or more is a sign of an approaching storm.

2.           Hydraulic Machines

• Whenever external pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions. This is the Pascal's law for transmission of fluid pressure and has many applications in daily life.
• A number of devices such as hydraulic lift and hydraulic brakes are based on the Pascal's law. In these devices fluids are used for transmitting pressure.
• Hydraulic brakes in automobiles also work on the same principle. When we apply a little force on the pedal with our foot the master piston moves inside the master cylinder, and the pressure caused is transmitted through the brake oil to act on a piston of larger area. A large force acts on the piston and is pushed down expanding the brake shoes against brake lining. In this way a small force on the pedal produces a large retarding force on the wheel.
• An important advantage of the system is that the pressure set up by pressing pedal is transmitted equally to all cylinders attached to the four wheels so that the braking effort is equal on all wheels.
• The Venturi-meter is a device to measure the flow speed of incompressible fluid.

3.           Blood Flow and Heart Attack

• Bernoulli's principle helps in explaining blood flow in artery. The artery may get constricted due to the accumulation of plaque on its inner walls.
• In order to drive the blood through this constriction a greater demand is placed on the activity of the heart. The speed of the flow of the blood in this region is raised which lowers the pressure inside and the artery may collapse due to the external pressure.
• The heart exerts further pressure to open this artery and forces the blood through. As the blood rushes through the opening, the internal pressure once again drops due to same reasons leading to a repeat collapse. This may result in heart attack.

4.           Viscosity

• Most of the fluids are not ideal ones and offer some resistance to motion. This resistance to fluid motion is like an internal friction analogous to friction when a solid moves on a surface. It is called viscosity. This force exists when there is relative motion between layers of the liquid.
• Suppose we consider a fluid like oil enclosed between two glass plates. The bottom plate is fixed while the top plate is moved with a constant velocity v relative to the fixed plate. If oil is replaced by honey, a greater force is required to move the plate with the same velocity. Hence we say that honey is more viscous than oil.
• When a fluid is flowing in a pipe or a tube, then velocity of the liquid layer along the axis of the tube is maximum and decreases gradually as we move towards the walls where it becomes zero.
• Generally thin liquids like water, alcohol etc. are less viscous than thick liquids like coal tar, blood, glycerin etc.
• Blood is 'thicker' (more viscous) than water. Relative viscosity $(\eta /{{\eta }_{water}})$ of blood remains constant between 0°C and 37°C. The viscosity of liquids decreases with temperature while it increases in the case of gases.

5.           Stokes' Law and Reynolds Number

• When a body falls through a fluid it drags the layer of the fluid in contact with it. A relative motion between the different layers of the fluid is set and as a result the body experiences a retarding force. Falling of a raindrop and swinging of a pendulum bob are some common examples of such motion.
• It is seen that the viscous force is proportional to the velocity of the object and is opposite to the direction of motion.
• A raindrop in air. It accelerates initially due to gravity. As the velocity increases, the retarding force also increases. Finally when viscous force plus buoyant force becomes equal to force due to gravity, the net force becomes zero and so does the acceleration.
• When the rate of flow of a fluid is large, the flow no longer remain laminar, but becomes turbulent. In a turbulent flow the velocity of the fluids at any point in space varies rapidly and randomly with time.
• The smoke rising from a burning stack of wood, oceanic currents are turbulent. Twinkling of stars is the result of atmospheric turbulence. The wakes in the water and in the air left by cars, aeroplanes and boats are also turbulent.
• Osborne Reynolds (1842-1912) observed that turbulent flow is less likely for viscous fluid flowing at low rates. He defined a dimensionless number, whose value gives one an approximate idea whether the flow would be turbulent. This number is called the Reynolds Re.
• Turbulence dissipates kinetic energy usually in the form of heat. Racing cars and planes are engineered to precision in order to minimise turbulence. The design of such vehicles involves experimentation and trial and error.
• Turbulence (like friction) is sometimes desirable. Turbulence promotes mixing and increases the rates of transfer of mass, momentum and energy. The blades of a kitchen mixer induce turbulent flow and provide thick milk shakes as well as beat eggs into a uniform texture.

6.           Surface Tension

• We have noticed that, oil and water do not mix; water wets you and me but not ducks: mercury does not wet glass but water sticks to it, oil rises up a cotton wick, inspite of gravity, Sap and water rise up to the top of the leaves of the tree, hairs of a paint brush do not cling together when dry and even when dipped in water but form a fine tip when taken out of it. All these and many more such experiences are related with the free surfaces of liquids.
• Liquids have no definite shape but have a definite volume, they acquire a free surface when poured in a container. These surfaces possess some additional energy. This phenomenon is known as surface tension and it is concerned with only liquid as gases do not have free surfaces.
• Surface tension is a force per unit length (or surface energy per unit area) acting in the plane of the interface between the plane of the liquid and any other substance; it also is the extra energy that the molecules at the interface have as compared to molecules in the interior.
• One consequence of surface tension is that free liquid drops and bubbles are spherical if effects of gravity can be neglected. You must have seen this especially clearly in small drops just formed in a high-speed spray or jet, and in soap bubbles blown by most of us in childhood.
• So for a given volume the surface with minimum energy is the one with the least area.
• So, if gravity and other forces (e.g. air resistance) were ineffective, liquid drops would be spherical. Another interesting consequence of surface tension is that the pressure inside a spherical drop is more than the pressure outside.
• One consequence of the pressure difference across a curved liquid-air interface is the wellknown effect that water rises up in a narrow tube in spite of gravity. The word capilla means hair in Latin.
• We clean dirty clothes containing grease and oil stains sticking to cotton or other fabrics by adding detergents or soap to water, soaking clothes in it and shaking.
• Washing with water does not remove grease stains. This is because water does not wet greasy dirt; i.e., there is very little area of contact between them. If water could wet grease, the flow of water could carry some grease away.
• The molecules of detergents are hairpin shaped, with one end attracted to water and the other to molecules of grease, oil or wax, thus tending to form water-oil interfaces.
• This kind of process using surface active detergents or surfactants is important not only for cleaning, but also in recovering oil, mineral ores etc.

7.           Blood Pressure

• In evolutionary history there occurred a time when animals started spending a significant amount of time in the upright position. This placed a number of demands on the circulatory system.
• The venous system that returns blood from the lower extremities to the heart underwent changes. We will recall that veins are blood vessels through which blood returns to the heart.
• Humans and animals such as the giraffe have adapted to the problem of moving blood upward against gravity. But animals such as snakes, rats and rabbits will die if held upwards, since the blood remains in the lower extremities and the venous system is unable to move it towards the heart.
• The human body is a marvel of nature. The veins in the lower extremities are equipped with valves, which open when blood flows towards the heart and close if it tends to drain down.
• Blood is returned at least partially by the pumping action associated with breathing and by the flexing of the skeletal muscles during walking. This explains why a soldier who is required to stand at attention may faint because of insufficient return of the blood to the heart. Once he is made to lie down, the pressures become equalized and he regains consciousness. I
• An instrument called the sphygmomanometer usually measures the blood pressure of humans. It is a fast, painless and non-invasive technique and gives the doctor a reliable idea about the patient's health. The measurement process.
• There are two reasons why the upper arm is used. First, it is at the same level as .the heart and measurements here give values close to that at the heart. Secondly, the upper arm contains a single bone and makes the artery there (called the brachial artery) easy to compress.
• We have all measured pulse rates by placing our fingers over the wrist. Each pulse takes a little less than a second. During each pulse the pressure in the heart and the circulatory system goes through a maximum as the blood is pumped by the heart (systolic pressure) and a minimum as the heart relaxes (diastolic pressure).
• The sphygmomanometer is a device, which measures these extreme pressures. It works on the principle that blood flow in the brachial (upper arm) artery can be made to go from laminar to turbulent by suitable compression. Turbulent flow is dissipative, and its sound can be picked up on the stethoscope.
• The blood pressure of a patient is presented as the ratio of systolic/diastolic pressures. For a resting healthy adult it is typically $120/80$mm of Hg $\left( 120/80\text{ }torr \right).$Pressures above $140/90$require medical attention and advice. High blood pressures may seriously damage the heart, kidney and other organs and must be controlled.

8.           Buoyancy

• A ship made of iron and steel does not sink in sea water, but while the same amount of iron and steel in the form of a sheet would sink? These questions can be answered by taking buoyancy in consideration.
• The nail sinks. The force due to the gravitational attraction of the earth on the iron nail pulls it downwards. There is an upthrust of water on the nail, which pushes it upwards. But the downward force acting on the nail is greater than the upthrust of water on the nail.
• The cork floats while the nail sinks. This happens because of the difference in their densities. The density of a substance is defined as the mass per unit volume. The density of cork is less than the density of water. This means that the upthrust of water on the cork is greater than the weight of the cork. So it floats.
• The density of an iron nail is more than the density of water. This means that the upthrust of water on the iron nail is less than the weight of the nail. So it sinks.
• Therefore object§ of density less than that of a liquid float on the liquid. The objects of density greater than that of a liquid sink in the liquid.
• Upward force exerted by water is known as the force of buoyancy.
• What is the magnitude of the buoyant force experienced by a body? Is it the same in all fluids for a given body? Do all bodies in a given fluid experience the same buoyant force?
• The answer to these questions is contained in Archimedes' principle, stated as follows: When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.
• Archimedes' principle has many applications. It is used in designing ships and submarines. Lactometers, which are used to determine the purity of a sample of milk and hydrometers used for determining density of liquids, are based on this principle.

9.           Important Facts

• Relative density is a ratio of similar quantities, it has no unit.
• The weight of an object is the force with which it is attracted towards the earth. It is denoted by W. As the weight of an object is the force with which it is attracted towards the earth. It has both magnitude and direction.
• The mass of an object remains the same everywhere, that is, on the earth and on any planet whereas its weight depends on its location.
• The mass of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on objects.
• The French scientist Blaise Pascal observed that the pressure in a fluid at rest is the same at all points if they are at the same height.
• For a liquid in equilibrium the pressure is same at all points in a horizontal plane.
• The Bernoulli's relation may be stated as follows: As we move along a streamline the sum of the pressure (P), the kinetic energy per unit volume ($\rho {{V}^{2}}/2$) and the potential energy per unit volume $(\rho gh)$ remains a constant. Bernoulli's equation ideally applies to fluids with zero viscosity or non-viscous fluids. Viscosity is like friction and it converted kinetic energy into heat energy.

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